Masks are used in the manufacture of semiconductors (e.g., computer chips) to produce features on a wafer. For example, masks may be used to etch features from resist that, when implemented, perform a variety of operations, such as logic operations using switches, gates, and so on. However, the functionality desired from semiconductors is ever increasing and therefore features are continually added to semiconductors to provide this functionality. Further, the size of these features is also ever decreasing to permit these additional features to be added to the semiconductors, to increase the speed at which the operations may be performed, and so on. Therefore, a mask may result in an intricate layout of relatively small and numerous features.
Validation techniques were developed to ensure that these features would be produced and therefore operate as desired, such as in a desired shape, size, spacing and so on. One such traditional technique sampled contours generated by a lithographic simulation of the mask at discrete locations on the desired layout. Measurements were then performed at these points in a limited number of directions to determine whether these sampled points complied with the desired structure, i.e., would form desired features of a semiconductor device. However, this validation was spatially discrete in that validation was typically performed using just these sampled points. Further, this validation technique was also constrained by the limited number of directions that were tested. Therefore, the use of discrete points and limited directions could miss violations of desired parameters during the validation process. Although the number of points sampled and/or the number of directions could be increased to increase accuracy, such an increase typically involved a significant increase in an amount of computing resources used to perform the validation. Therefore, this traditional technique typically involved a tradeoff between accuracy desired and the amount of resources that were available.
The same reference numbers are utilized in instances in the discussion to reference like structures and components.